Chaos synchronization of unified chaotic systems via LMI

Kuntanapreeda, Suwat

doi:10.1016/j.physleta.2009.06.006

Cited by 49 publications

(26 citation statements)

References 24 publications

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“…Next, we shall give the following corollary that proves that the coexistence of synchronization and anti-synchronization in the unified chaotic systems is realized by the above controller u = (k 2 E 1 , 0, 0) T , where x 1 , x 2 anti-synchronizes y 1 , y 2 while x 3 synchronizes y 3 , respectively. (17), the orbits (E(t), e(t)) T converge to origin as t → ∞, implying that the coexistence of synchronization and anti-synchronization in the unified chaotic systems is realized by the controller u = (k 2 E 1 , 0, 0) T .…”

Section: Theorem 13 Starting From Any Initial Values Of the Controllementioning

confidence: 99%

Coexistence of synchronization and anti-synchronization in chaotic systems

Ren

Guo

Vincent

2016

Archives of Control Sciences

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The coexistence of anti-synchronization and synchronization in chaotic systems is investigated. A novel algorithm is proposed to determine the variables of the master system that should anti-synchronize with corresponding variables of the slave system. Control strategies that guarantee the coexistence of synchronization and anti-synchronization in the unified chaotic system are presented; while numerical simulations are employed to validate and illustrate the effectiveness of the proposed method.

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Section: Theorem 13 Starting From Any Initial Values Of the Controllementioning

confidence: 99%

Coexistence of synchronization and anti-synchronization in chaotic systems

Ren

Guo

Vincent

2016

Archives of Control Sciences

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“…Remark 1. In [10] and [18], trajectories of chaotic systems were assumed to be bounded which were used to derive the synchronization criteria. However, it is difficult or impossible to estimate the bound of trajectories of two coupled systems (2) and (3).…”

Section: Synchronization Criteriamentioning

confidence: 99%

“…However, it is difficult or impossible to estimate the bound of trajectories of two coupled systems (2) and (3). Compared with synchronization criteria in [10] and [18], the norm bounds of trajectories of systems (2) and (3) are not used to derive synchronization criteria in Proposition 1, and gains k 0 and k are dependent on system constants a, b, c and p which is the main contribution of this paper.…”

Section: Synchronization Criteriamentioning

confidence: 99%

“…Hrg (2013) [8] investigated synchronization of two HR neurons, but the couplings between two neurons were unidirectional. Kuntanapreeda [10] studied synchronization of two unified chaotic systems in which the control method can be applied to studying the master-slave synchronization of HR neurons. Nguyen and Hong [18] investigated synchronization of chaotic FitzHugh-Nagumo neurons which were the special cases of HR neurons.…”

Section: Introductionmentioning

confidence: 99%

“…Nguyen and Hong [18] investigated synchronization of chaotic FitzHugh-Nagumo neurons which were the special cases of HR neurons. In [10,18], the norm bounds of state variables of both controlled and uncontrolled chaotic systems were used to derive synchronization criteria. However, it is difficult or impossible to estimate the norm bounds of state variables of two coupled HR neurons (controlled DOI: 10.14736/kyb-2015- and uncontrolled HR neurons).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Synchronization of two coupled Hindmarsh-Rose neurons

Ding¹,

Han²

2015

Kybernetika

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Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

Mobayen

Tchier

2017

Asian Journal of Control

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This paper proposes a new state-feedback stabilization control technique for a class of uncertain chaotic systems with Lipschitz nonlinearity conditions. Based on Lyapunov stabilization theory and the linear matrix inequality (LMI) scheme, a new sufficient condition formulated in the form of LMIs is created for the chaos synchronization of chaotic systems with parametric uncertainties and external disturbances on the slave system. Using Barbalat's lemma, the suggested approach guarantees that the slave system synchronizes to the master system at an asymptotical convergence rate. Meanwhile, a criterion to find the proper feedback gain vector F is also provided. A new continuous-bounded nonlinear function is introduced to cope with the disturbances and uncertainties and obtain a desired control performance, i.e. small steady-state error and fast settling time. Several criteria are derived to guarantee the asymptotic and robust stability of the uncertain master-slave systems. Furthermore, the proposed controller is independent of the order of the system's model. Numerical simulation results are displayed with an expected satisfactory performance compared to the available methods.

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Chaos synchronization of unified chaotic systems via LMI

Cited by 49 publications

References 24 publications

Coexistence of synchronization and anti-synchronization in chaotic systems

Coexistence of synchronization and anti-synchronization in chaotic systems

Synchronization of two coupled Hindmarsh-Rose neurons

Synchronization of A Class of Uncertain Chaotic Systems with Lipschitz Nonlinearities Using State‐Feedback Control Design: A Matrix Inequality Approach

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